Protesters who brought central Kiev to a halt in support of challenger Viktor Yushchenko confronted riot police by the president's offices on Wednesday.
Political tensions mounted on Tuesday night after Yushchenko proclaimed himself president and swore himself in.
By 6.30am (0430 GMT) on Wednesday, groups of protesters were out again on the streets, marching up and down Kiev's main mall, Khreshchatyk, and chanting the opposition leader's name.
Yushchenko supporters, easily recognisable by the vivid orange campaign colours that they wear, plan to head for the president's offices again later in the day.
But incomplete official results, still to be confirmed as final by election officials, show Prime Minister Viktor Yanukovich poised to win Sunday's run-off vote between the rivals who stand for different images for the future of Ukraine.
Prime Minister and disputed winning presidential candidate Yanukovich sees future prosperity in closer ties with Russia.
Opposition leader Yushchenko favours gradual integration with Western Europe, but recognises Russia as a "strategic partner".
Ignoring the dispute, Yushchenko
has already sworn himself in
Outgoing President Leonid Kuchma called for talks with all parties to solve the election row and dismissed the opposition protests as a "political farce".
Kuchma, who backed his prime minister in the race against Yushchenko, made it plain in a statement read on state television that he would not yield to the protesters.
However, parliamentarian Yulia Tymoshenko, a close aide to Yushchenko, told crowds: "We'll give Kuchma time to work out his proposals. Let no one say we came here in vain. They're afraid. They're on the defensive."
Her attempts to persuade the police to join the protest recalled scenes that led to the fall of Georgian president Eduard Shevardnadze exactly a year ago.
Other Yushchenko allies said they would elaborate on their strategy on Wednesday at Independence Square, that drew up to 200,000 people on Tuesday.